Two guns A and B can fire bullets at speeds 2Km/s and 4Km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum area covered by the bullets fired by the two guns on the ground is 1x, then the value of x is ____

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Two guns A and B can fire bullets at speeds 2Km/s and 4Km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum area covered by the bullets fired by the two guns on the ground is $\frac{1}{x},$ then the value of x is _____.

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answer is 16.

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Detailed Solution

$R = \frac{u^{2} \sin^{2} θ}{g}$
For max area R should be max $\Rightarrow θ = 45^{o}$
$\frac{A_{1}}{A_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}} = \frac{{(u_{1}^{2})}^{2}}{{(u_{2}^{2})}^{2}} = {(\frac{u_{1}}{u_{2}})}^{4} = {(\frac{2}{4})}^{4} = \frac{1}{16}$